NeuroImage 18 (2003) 865– 879
www.elsevier.com/locate/ynimg
Factors affecting the accuracy of near-infrared spectroscopy
concentration calculations for focal changes in oxygenation parameters
Gary Strangman,a,b,* Maria Angela Franceschini,b,c and David A. Boasb
a
Neural Systems Group, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129, USA
Athinoula A. Martinos Center, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129, USA
c
Bioengineering Center, Department of Electrical Engineering and Computer Science, Tufts University, 4 Colby Street, Medford, MA 02155-6013, USA
b
Received 28 January 2002; revised 25 October 2002; accepted 21 November 2002
Abstract
Near-infrared spectroscopy (NIRS) can be used to noninvasively measure changes in the concentrations of oxy- and deoxyhemoglobin
in tissue. We have previously shown that while global changes can be reliably measured, focal changes can produce erroneous estimates
of concentration changes (NeuroImage 13 (2001), 76). Here, we describe four separate sources for systematic error in the calculation of focal
hemoglobin changes from NIRS data and use experimental methods and Monte Carlo simulations to examine the importance and mitigation
methods of each. The sources of error are: (1) the absolute magnitudes and relative differences in pathlength factors as a function of
wavelength, (2) the location and spatial extent of the absorption change with respect to the optical probe, (3) possible differences in the
spatial distribution of hemoglobin species, and (4) the potential for simultaneous monitoring of multiple regions of activation. We found
wavelength selection and optode placement to be important variables in minimizing such errors, and our findings indicate that appropriate
experimental procedures could reduce each of these errors to a small fraction (⬍10%) of the observed concentration changes.
© 2003 Elsevier Science (USA). All rights reserved.
Introduction
Diffuse optical methods—whereby light is transmitted
through a highly scattering medium for the purpose of
making a measurement of that medium— have been in use
for over two decades to monitor important hemodynamic
variables in tissue. These measurements are made possible
by an “optical window” in tissue that spans the near-infrared
region (approximately 650 –950 nm) of the electromagnetic
spectrum. In this region, oxyhemoglobin (HbO2) and deoxyhemoglobin (HbR) are the dominant absorbers, and their
concentrations are sufficiently low (⬍100 ␮M) to allow
light to pass through several centimeters of tissue and still
be detected (Gratton et al., 1994; cf. Jobsis, 1977). The
promise of diffuse optical methods lies in their potential to
provide absolute quantitation of hemodynamic variables,
including [HbO2] and [HbR] (and the sum of these compo* Corresponding author. Neural Systems Group, 149 13th Street, Room
9103, Charlestown, MA 02129. Fax: ⫹1-617-726-4078.
E-mail address: [email protected] (G. Strangman).
nents, total hemoglobin, [HbT]), as well as potentially cytochrome oxidase concentrations (Cope et al., 1991; Elwell
et al., 1994; Hock et al., 1995; Hueber et al., 2001; Kohl et
al., 1998; Kurth et al., 1993; Quaresima et al., 1998; Tamura
et al., 1997).
Near-infrared spectroscopy (NIRS) is an increasingly
popular, noninvasive method for monitoring these hemodynamic variables. NIRS has been used in a variety of applications including fetal monitoring (e.g., Aldrich et al., 1994;
Parilla et al., 1997; Peebles et al., 1992), cardiac surgery (for
a review, see Nollert et al., 2000), muscle monitoring (e.g.,
Chance, 1991; Duncan et al., 1995; Franceschini et al.,
1997; Nioka et al., 1998), and a wide variety of studies on
brain function (cf. Chance, 1991; Villringer and Chance,
1997). To accurately quantify [HbR] and [HbO2], the relative contributions of these two absorbers must be separated
from the raw optical signals. To do so, measurements at two
or more wavelengths are simultaneously acquired, and a
model is applied to convert the wavelength data to chromophore concentrations.
The standard model used to perform this conversion is
1053-8119/03/$ – see front matter © 2003 Elsevier Science (USA). All rights reserved.
doi:10.1016/S1053-8119(03)00021-1
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G. Strangman et al. / NeuroImage 18 (2003) 865– 879
based on the modified Beer–Lambert law (MBLL; Delpy et
al., 1988). This model is highly dependent on knowledge
about the spatial location and extent of any change in [HbR]
and/or [HbO2] within the light-sampling region. For some
measures—for example, in muscle—the simple assumption
that concentration changes are global within the tissue may
hold to a reasonable degree. For measurements in other
settings, however, such as functional brain activation, this
assumption is clearly violated. In an adult human, the scalp
and skull range from approximately 1 to 2 cm thick, depending on the subject and the region on the head. Consistent negative findings from whole-head functional MRI
scanning indicate that these layers often exhibit little or no
change in hemodynamic variables during a wide variety of
tasks. Even within the brain, while gray matter exhibits
substantial changes under functional loading, the activated
regions are commonly less than 1 cm across—a spatial scale
that is focal relative to the sampling region with sourcedetector separations ranging from 2 to 5 cm. Hence, the
activated region in this situation will constitute only a small
fraction—less than 10%— of the entire sampling region.
In a previous report (Boas et al., 2001), we demonstrated
that when deriving ⌬[HbR] and ⌬[HbO2] from NIRS data
using the MBLL with a global-change assumption, serious
errors can arise when such a focal change is actually
present. These errors are systematic and are a function of the
positioning of the source and detector relative to the focal
change in chromophores. We argued that, as a consequence
of the changes being local and unknown in position relative
to the source and detector, [HbR] and [HbO2] cannot, in
general, be quantified in an absolute sense by NIRS. We
also argued that imaging (as opposed to point measurements) is one solution to this quantification problem.
In this article, we elaborate on our previous findings by
pointing out other potential sources of systematic error in
computing concentrations as well as by providing guidelines for reducing such errors in the absence of imaging. To
do so will first require two definitions. The differential
pathlength factor (DPF) is the scaling factor that relates
source-detector separations to the average path length light
travels between the source and detector. The DPF is a
function of wavelength and can be measured by time-domain and frequency-domain systems. Tabulated values exist
for various tissues (Duncan et al., 1995; Essenpreis et al.,
1993), although the values do vary across subjects and over
time even for a given subject and tissue (Duncan et al.,
1996). The notion of a DPF implies the assumption that the
chromophore change is global to the sampling region. In
contrast, the term partial pathlength factor (PPF) will refer
to a similar scaling factor, but one that instead assumes a
focal change. A PPF therefore represents a proportionality
factor converting the source-detector separation into the
average path length that light travels through a focal region
of chromophore change (Hiraoka et al., 1993; Steinbrink et
al., 2001).
We argue that there are four potential sources of error to
be considered when analyzing raw NIRS data using the
MBLL. They are as follows: (1) the absolute magnitudes
and relative differences in pathlength factors as a function
of wavelength, (2) the location and spatial extent of the
absorption change with respect to the optical probe and the
resulting PPFs, (3) possible differences in the spatial distribution of hemoglobin species and the resulting speciesspecific PPFs (e.g., PPFHbR and so on), and (4) the potential
for simultaneous monitoring of multiple regions of activation. The optical researcher’s goal is to minimize the effect
of any such errors. We demonstrate both empirically (in
particular see Fig. 3) and with simulations that wavelength
selection (point 1, above) is an important parameter—suggesting that proper wavelength selection can help to minimize PPF-related systematic errors. We also show experimental evidence that simply optimizing optical signals (i.e.,
optimizing optode position relative to the focal change) can
also minimize PPF-related systematic errors (point 2). We
quantify the effects related to all four points via several
Monte Carlo simulations on a realistic head model that
examine the sensitivity of optical analysis to the effects of
spatial location, differential species distribution, and multiple activation sites. In summary, we found that careful
experimental choices should limit these errors to a small
fraction (⬍10%) of the observed concentration changes.
Theory of the modified Beer–Lambert law
The modified Beer–Lambert law is typically used to
describe the change in light attenuation in scattering media
because of absorption changes (which in turn result from
changes in chromophore concentrations). When the change
in absorption is global throughout the medium, then the
MBLL is written as
⌬OD共 ␭ 兲 ⫽ ⌬ ␮ a共 ␭ 兲 LᐉDPF共 ␭ 兲 ⫽ 关␧ HbO2共 ␭ 兲⌬关HbO2兴
⫹ ␧ HbR共 ␭ 兲⌬关HbR兴兴LᐉDPF共 ␭ 兲,
(1)
where ⌬OD(␭) is the change in optical density measured at
a given wavelength, ⌬␮a(␭) is the corresponding change in
tissue absorption, L is the separation between the source and
detector, and ᐉDPF(␭) is the differential pathlength factor
(unitless), which accounts for the increased distance that
light travels from the source to the detector because of
scattering and absorption effects (in the presence of no
scattering ᐉDPF(␭) ⫽ 1). As shown in the second line, the
change in absorption is related to changes in the chromophore concentrations of oxyhemoglobin (⌬[HbO2]) and
deoxyhemoglobin (⌬[HbR]) by the extinction coefficients
␧HbO2(␭) and ␧HbR(␭), which are wavelength dependent.
From measurements of ⌬OD(␭) at two wavelengths, the
concentration changes are given by
G. Strangman et al. / NeuroImage 18 (2003) 865– 879
⌬[HbR] ⫽
␧HbO2(␭2)⌬␮a(␭1) ⫺ ␧HbO2(␭1)⌬␮a(␭2)
␧HbR(␭1)␧HbO2(␭2) ⫺ ␧HbO2(␭1)␧HbR(␭2)
⌬[HbO2] ⫽
␧HbR(␭1)⌬␮a(␭2) ⫺ ␧HbR(␭2)⌬␮a(␭1)
.
␧HbR(␭1)␧HbO2(␭2) ⫺ ␧HbO2(␭1)␧HbR(␭2)
(2)
When the change in absorption is not global, the modified
Beer–Lambert law can be rewritten as
冘⌬␮ 共␭兲ᐉ
N
⌬OD共 ␭ 兲 ⫽ L
a,i
PPF,i
冘关␧
共 ␭ 兲⌬关HbO2兴
i⫽1
⫹ ␧ HbR共 ␭ 兲⌬关HbR]]ᐉPPF,i共 ␭ 兲,
(3)
where ᐉPPF,i(␭) is the partial pathlength factor (unitless)
through a region of uniform absorption change. A sum is
performed over N regions of uniform absorption change.
This notation has been used by Steinbrink et al. (2001) to
study the sensitivity to tissue layers at different depths.
In the case of brain activation, the measured change in
optical density is best analyzed with a PPF, because of the
focal nature of the brain activation. Unfortunately, accurate
estimation of the PPF is not feasible because it requires
knowledge of the position and spatial extent of the local
absorption change, as well as the optical properties of the
surrounding tissue. For this reason, the DPF is used in most
analyses (e.g., Franceschini et al., 2000; Tamura et al.,
1997).
Systematic errors in the choice of the pathlength factor
result in systematic errors in the estimated concentration
changes, which can lead to cross-talk between species in the
estimated concentration changes (e.g., Boas et al., 2001).
For example, if we measure the change in optical density
due to a local absorption change (⌬ODreal as given by Eq.
(3)) and compare that to an estimate of the absorption
change using the differential pathlength factor (⌬ODestim as
given by Eq. (1)) we find that we underestimate the absorption change. That is, we assume that ⌬ODestim ⫽ ⌬ODreal,
and as a result we obtain the following expression for our
underestimation:
ᐉPPF(␭)
⌬␮a,real(␭).
ᐉDPF(␭)
P⫽
冋
⫺k共 ␭ 1兲␧ X共 ␭ 1兲␧ O共 ␭ 2兲 ⫹ k共 ␭ 2兲␧ O共 ␭ 1兲␧ X共 ␭ 2兲
关␧ O共 ␭ 1兲␧ X共 ␭ 2兲 ⫺ ␧ X共 ␭ 1兲␧ O共 ␭ 2兲兴
(4)
The estimated absorption change (⌬␮a,estim) will always be
smaller than the real absorption change because the PPF is
always smaller than the DPF. Thus, the estimated concentration changes will always be smaller than the real concen-
册
⫽ Ak共 ␭ 1兲 ⫹ Bk共 ␭ 2兲
C⫽
⫺␧ O共 ␭ 1兲␧ O共 ␭ 2兲
关k共 ␭ 1兲 ⫺ k共 ␭ 2兲兴
␧ O共 ␭ 1兲␧ X共 ␭ 2兲 ⫺ ␧ X共 ␭ 1兲␧ O共 ␭ 2兲
⫽ D关k共 ␭ 1兲 ⫺ k共 ␭ 2兲兴,
Cross-talk between oxy- and deoxyhemoglobin
⌬␮a,estim(␭) ⫽
(5)
where [X] represents either [HbO2] or [HbR] and correspondingly [O] represents the other species [HbR] or
[HbO2], respectively. P indicates the partial volume reduction in the estimated species concentration and C indicates
the cross-talk from the other species, as given by
N
HbO2
tration changes. This is more generally known as a partial
volume effect.
The potential for cross-talk between the estimated oxyand deoxyhemoglobin concentrations is found by first relating the estimated concentration changes to the estimated
absorption changes (Eq. (2)), substituting the real absorption change for the estimated absorption change using Eq.
(4), and then substituting the real concentration changes for
the real absorption changes (as done in Eq. (1)). A few lines
of algebra indicates that
⌬[X]estim ⫽ P⌬[X]real ⫹ C⌬[O]real,
共␭兲
i⫽1
⫽L
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(6)
where k(␭) ⫽ ᐉPPF(␭)/ᐉDPF(␭) (or more generally written as
k(␭) ⫽ ᐉreal(␭)/ᐉestim(␭)) indicates the error in the pathlength
factor (or the partial volume effect) at each wavelength.
Note that when the error at each wavelength is the same, the
cross-talk C ⫽ 0. The parameters A, B, and D are simply a
function of wavelength and are plotted in Fig. 4c for HbO2
(left) and HbR (right).
Cross-talk from species-dependent pathlength factors
Now consider the possibility that a localized brain activation results in oxy- and deoxyhemoglobin changes with
different spatial locations and/or spatial extents. For example, the [HbR] change appears predominantly in the venous
compartment while the [HbO2] change appears in all vascular compartments. Moreover, there are experimental indications that the region of HbO2 change during functional
activation is spatially larger than that of HbR (e.g., Duong
et al., 2000; Franceschini et al., 2000; Hu et al., 1997). In
this case, we need different PPFs for each species. Considering only one region of activation, we then have
⌬ODreal(␭) ⫽ [␧HbO2(␭)⌬[HbO2]ᐉPPF, HbO2(␭)
⫹ ␧HbR(␭)⌬[HbR]ᐉPPF, HbR(␭)]L, and
⌬␮a,estim(␭) ⫽
(7a)
ᐉPPF, HbO2(␭)
⌬␮a,HbO2(␭)
ᐉDPF(␭)
⫹
ᐉPPF, HbR(␭)
⌬␮a,HbR(␭)
ᐉDPF(␭)
(7b)
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G. Strangman et al. / NeuroImage 18 (2003) 865– 879
By substituting Eq. (7b) into Eq. (2), errors in our estimate
of the pathlength factor will still produce errors in the
estimated concentration change according to Eq. (5) but
with
P ⫽ Ak X共 ␭ 1兲 ⫹ Bk X共 ␭ 2兲
C ⫽ D关k O共 ␭ 1兲 ⫺ k O共 ␭ 2兲兴
(8)
A, B, and D have the same form as in Eq. (6). The error in
the pathlength factor is now species dependent where X
indicates the same species and O indicates the other species
(see Eq. (5)), such that kX(␭) ⫽ ᐉPPF,X(␭)/ᐉDPF,X(␭) and
kO(␭) ⫽ ᐉPPF,O(␭)/ᐉDPF,O(␭). More generally, the subscripts
PPF and DPF could be replaced with real and estimated,
respectively. Once again note that when the PPF-related
error at each wavelength is the same, the cross-talk C ⫽ 0.
Cross-talk between two different activation regions
Finally, consider the possibility of a brain stimulus resulting in two separate activation foci (labeled ␣ and ␤). In
this case,
⌬ODreal(␭) ⫽ [␧HbO2(␭)⌬[HbO2]␣
⫹ ␧HbR(␭)⌬[HbR]␣]ᐉPPF,␣(␭)L
⫹ [␧HbO2(␭)⌬[HbO2]␤
⫹ ␧HbR(␭)⌬[HbR]␤]ᐉPPF,␤(␭)L.
(9)
Errors in the estimate of the pathlength factors will then
produce errors in the estimate of the concentration change at
one focus of the form
⌬[X]estim,␣ ⫽ P ␣⌬[X]real,␣ ⫹ C ␣⌬[O]real,␣
⫹ P ␤⌬[X]real,␤ ⫹ C ␤⌬[O]real,␤,
(10)
where P␣ and C␣ are given by Eq. (6) but with k(␭) ⫽ k␣(␭)
⫽ ᐉPPF,␣(␭)/ᐉDPF,␣(␭). P␤ and C␤ are also given by Eq. (6)
but with k(␭) ⫽ k␤(␭) ⫽ ᐉPPF,␤(␭)/ᐉDPF,␤(␭).
Materials and methods
To examine the quantitative importance of these theoretical derivations, we performed two types of studies: (1)
NIRS experiments using a simple motor task designed to
illustrate the theoretical points and (2) several Monte Carlo
simulations on a tissue-segmented model based on an individual MRI scan to help quantify the effect of the four
described sources of errors in a general NIRS-type experiment.
NIRS
Instrumentation and setup
A simple, unimanual motor task was used to examine the
cross-talk in calculating [HbR] and [HbO2] for different
wavelength pairs. The study was approved by the Institutional Review Board of Tufts University, where the human
experiments were performed, and all subjects (three men,
ages 27, 29, and 54 years) gave their written informed
consent. An ISS frequency-domain tissue spectrometer
(Model 96208, ISS, Inc., Champaign, IL) was used for the
NIRS recording. Two source fibers were attached to an
elastic cap and positioned 1.6 and 2.8 cm posterior to
position C3 in the EEG 10 –20 system, because it has been
shown that C3 lies approximately over the hand area of the
left primary motor cortex (Steinmetz et al., 1989). Each
source was composed of eight laser diodes emitting at 636,
675, 691, 752, 780, 788, 830, and 840 nm, respectively,
which were fed into a 2-mm bifurcated fiber. One detector
fiber, 3 mm in diameter, was also attached to the elastic cap,
positioned 1.8 cm anterior to C3 (on the line formed by C3
and the sources). We report experimentally calculated
[HbR] and [HbO2] results for just 691, 752, and 780 nm
paired with 830 nm because of (1) low signal amplitudes
from 636 and 675 nm, (2) signals from 788 and 840 nm
were virtually identical to those collected at 780 and 830,
respectively, and (3) to improve figure clarity.
DPF measurement
Prior to commencing each NIRS recording, DPFs were
measured by quantifying the tissue absorption coefficient
and the reduced scattering coefficient using the frequencydomain multidistance method (for details, see Fantini et al.,
1994). This method allows determination of the DPF at
multiple wavelengths in the absence of a measure of absolute phase, as is the case for the ISS instrument. The multidistance scheme was implemented by considering the data
collected by the two source fibers located at two different
distances (3.6 and 4.8 cm) from the detector fiber. Details on
this hybrid frequency-domain (to measure the DPF) and
continuous-wave (modified Beer–Lambert law) approach
have been described elsewhere (Fantini et al., 1999). To
determine the DPF at the eight wavelengths we averaged
200 points during 32 s of baseline (the 16 lasers were turned
on one at a time for 10 ms each, i.e., acquisition time per
data point 160 ms). Once the DPF was measured, we turned
off the source at the larger distance from the detector and
acquired NIRS data from each of the eight wavelengths
every 80 ms.
Protocol
During the experiment, the subject was asked to rest
quietly in a supine position. When the experimental run
began, the subject alternated between rest for 17 s and 15 s
of four-finger flexion/extension with the four fingers of the
right hand. The subject performed 10 such 15-s blocks of
the motor task, interleaved with 11 blocks of rest, for a total
run length of 337 s. The resulting motor-task data were
time-trigger averaged separately for each wavelength on the
onset of motor activation. Thus, each data point in the
reported time series represents an average of 10 points in the
G. Strangman et al. / NeuroImage 18 (2003) 865– 879
original data. Six time series pairs (830 nm paired with each
wavelength below 800 nm) were analyzed using the MBLL.
Each subject was tested twice with a slightly different probe
positions (⬃1-cm displacement). Our measure of concentration change was an average of the period from 10 to
12.4 s (30 data points) following the start of the stimulus,
having first zero-corrected concentrations at time 0 s. We
simultaneously measured pulse oximetry (Nelcore N-200)
and respiration (Sleep-mate/Newlife Technologies, RespEZ) on all subjects.
Monte Carlo simulations
General approach
The rules used for photon migration as employed in any
Monte Carlo program are described by Jacques and Wang
(1995) and Wang et al. (1995). To summarize, the initial
position and direction of the photon are defined as coming
from a point source with a defined direction and entering the
medium on the surface. Given the initial position and direction of the photon, the length to the first scattering event,
L, is calculated from an exponential distribution. Absorption
of the photon is considered by decreasing the photon weight
by exp(⫺␮aL), where ␮a is the absorption coefficient and L
is the length traveled by the photon (Wang et al., 1995). The
photon is moved this distance through the tissue and then a
scattering angle is calculated using the probability distribution given by the Henyey–Greenstein phase function (Wang
et al., 1995), and a new scattering length is determined from
an exponential distribution. The photon is propagated this
new distance in the new direction. This process continues
until the photon exits the medium or has traveled longer
than 10 ns, because the probability of photon detection in
tissue after such a period of time is exceedingly small.
When the photon does try to leave the medium, the probability of an internal reflection is calculated using Fresnel’s
equation (Haskell et al., 1994; Wang et al., 1995). If a
reflection occurs, the photon is reflected back into the medium and migration continues. Details about the Monte
Carlo code can be found in Boas et al. (2002). We use the
Monte Carlo approach here, instead of the Born approximation used in Boas et al. (2001), because Monte Carlo
methods provide an accurate solution of photon migration
through the head that is not biased by diffusion approximations. Previous work of this sort has examined partial volume effects (e.g., Okada et al., 1997) and spatial sensitivity
patterns from diffuse optical probes (e.g., Firbank et al.,
1998; Okada et al., 1997). To estimate the variability in our
Monte Carlo results, we ran multiple, independent simulations each with a new random number seed.
Anatomical head segmentation and associated Monte
Carlo parameters
Fig. 1 shows examples of the various Monte Carlo simulations. Each was performed on an anatomical MRI of a
human head, 1 ⫻ 1 ⫻ 1 mm resolution that was semiau-
869
tonomously segmented into six tissue types (air, scalp,
skull, cerebral spinal fluid, gray/white matter, and activated
brain tissue). To summarize the segmentation process, three
anatomical scans were obtained on a Siemens Sonata 1.5T
MRI scanner (T1-EPI, TR ⫽ 8 s, TE ⫽ 39 ms, ␪ ⫽ 90°, 27
slices, thickness 5 mm, skip 0.75 mm; T2-FSE, TR ⫽ 10 s,
TE ⫽ 48 ms, ␪ ⫽ 120°, 27 slices, thickness 5 mm, skip 0.75
mm; 3D SPGR, TR ⫽ 7.25 ms, TE ⫽ 3.2 ms, ␪ ⫽ 7°, 128
partitions, effective thickness 1.33 mm) and were then
coregistered. Separate measures and thresholds were used
for each tissue type (air ⫽ all, scalp ⫽ T2, skull ⫽ SPGR/
T2, CSF ⫽ T2/SPGR, brain ⫽ SPGR) resulting in all voxels
labeled as one of these five tissue types. To these tissue
types we artificially added a tissue type for activated brain
tissue (a subset of brain tissue voxels), the size and location
of which differed across simulations (see below). The contour overlay in Fig. 1 indicates the photon migration spatial
sensitivity profile for continuous-wave measurements produced by Monte Carlo simulation. One contour line is
shown for each half order of magnitude (10 dB) change in
the sensitivity of OD to changes in ␮a, and the contours end
after 5 orders of magnitude (100 dB). For all our simulations, we needed to assume values for ␮s⬘ and ␮a for each
tissue type and each wavelength. Given the wide variation
the ␮a and ␮s⬘ parameters that have been reported (e.g.,
Bevilacqua et al., 1999; Okada et al., 1997; Torricelli et al.,
2001), we chose the intermediate values found in Table 1
(where HbT is total hemoglobin and StO2 is the tissue oxygen
saturation). We approximated the wavelength dependence of
␮s⬘ by ␮s⬘(␭) ⫽ ␮s⬘(690) ⫺ 0.01 * (␭ ⫺ 690)—a linear approximation being adequate for the narrow wavelength range we are
considering—where ␮s⬘(690) came from Farrell et al. (1992).
Probe geometry
We employed several different probe geometries, depending on the systematic error under investigation. For
simulations of position, we kept the region of functional
activation fixed and moved the source-detector pair in
0.5-cm increments along the surface of the head, always
maintaining the 3-cm source-detector separation. Probe
movements were made in both the medial–lateral direction
(with extremes shown Figs. 1a and b) and the anterior–
posterior direction (i.e., through plane, not shown). For
simulations investigating species distribution and dual activations, only one probe location was used, namely the one
where the primary activation was approximately centered
below and between the source-detector pair and again the
source-detector separation was maintained at 3 cm.
Simulated brain activation
Regions of brain activation were chosen to be braintissue-only voxels within cubical blocks located at the surface of the cortex. Thus, for simulation purposes the activation existed only in anatomically defined brain and not in
CSF or overlying tissues. For the species distribution simulations, the volume of HbR change was fixed (specifically
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G. Strangman et al. / NeuroImage 18 (2003) 865– 879
Fig. 1. Illustrations of the extreme cases for the three types of Monte Carlo simulations. (a and b) The two extremes in simulation geometry for position, shown
for medial–lateral probe movement. White indicates the (fixed) region of activation, and contours indicate the source-detector probe sensitivity pattern. (c
and d) The two extremes in HbO2-region size for the simulations of noncoincident HbR–HbO2 changes. White indicates region of HbR ⫹ HbO2 change, while
the darker surround indicates the extended region of HbO2 change. (e and f) The two extremes in location of a secondary region of activation for the
dual-activation focus simulations. Primary region of activation is fixed below and between the source and detector; the darkest region in (e) indicates an
overlap between secondary and primary activations.
to that shown in Fig. 5a), encompassing a volume of 648
mm3. The volume of HbO2 change, in contrast, was increased in square shells (adding 1 mm inferior and medial to
the existing activation). The resulting eight volumes were
878, 1140, 1430, 1759, 2131, 2555, 3038, and 3560 mm3 in
size. The two extremes are depicted in Figs. 1c and d. For
the dual-activation conditions, the first, primary activation
assumed colocalized HbR and HbO2 changes, positioned at
the HbR location just described. The secondary activation
also assumed colocalized HbR and HbO2 changes and was
moved in five steps from the location of the first, 5 mm
medially and 2.5 mm superiorly per step, along the surface
of the brain (extremes are again shown in Figs. 1e and f).
The volume of this secondary activation was 614 mm3 (at
the point of maximum overlap or 5 mm lateral displacement), 654, 608, 728, and finally 594 mm3 at 25 mm
displacement.
Monte Carlo data analysis
Three main measures were computed from the Monte
Carlo data: DPF, PPF, and cross-talk. The DPF for a given
source-detector pair was calculated as the actual mean pathlength traveled by all photons leaving the source that
reached the detector, divided by the source-detector separation (30 mm). The PPF was calculated as the mean pathlength traveled through a given region of activation (i.e.,
regions of concentration change) of these same photons,
also divided by the source-detector separation. Cross-talk
Table 1
Monte Carlo simulation parameters (␮a,/␮s⬘, both in cm⫺1)
Region/parameter
690 nm
760 nm
780 nm
830 nm
[HbT] (␮M)
StO2 (%)
Scalp
Skull
Cerebrospinal fluid
Brain (gray ⫹ white)
0.159/8.0
0.101/10.0
0.004/0.1
0.178/12.5
0.177/7.3
0.125/9.3
0.021/0.1
0.195/11.8
0.164/7.1
0.115/9.1
0.017/0.1
0.170/11.6
0.191/6.6
0.136/8.6
0.026/0.1
0.186/11.1
75
75
0
75
75
75
0
65
G. Strangman et al. / NeuroImage 18 (2003) 865– 879
between species was determined by calculating C from Eqs.
(4) and (5).
Results
Wavelength selection
NIRS in vivo measurements
Fig. 2 shows the block-averaged results from an example
subject during the motor task, selecting the NIRS detector
showing the maximum signal modulation from baseline
during motor activity. Fig. 2a shows the measured DPF
values at each of eight wavelengths for an example subject.
The absolute values of these measures are above reported
values (Duncan et al., 1996), resulting from small (1–2
mm), random errors in the source-detector separation measurement. The spectral dependence of the DPF values, however, agree to within ⬃20% with those found in the literature, and it is the spectral dependence that is relevant to the
present results. Fig. 2a also shows an “altered” version of
the DPFs wherein the value for 830 was reduced by 10%
and the values at the other three wavelengths considered
were increased by 10% (for a 20% total difference, per
literature variation). The altered DPFs provide a rough indication about the sensitivity of our computed concentrations to typical variations in the pathlength factor. In Figs.
2b– d, the red and orange lines represent the calculated
concentration change in HbO2 using the measured and altered DPFs, respectively. Notice that ⌬[HbO2] differs when
modulating the DPF, but the relative magnitude of this
change is small. Similarly, the dark and light blue lines
show the calculated ⌬[HbR] using the measured versus
altered DPF, respectively. Notable with the 780- and
830-nm wavelength pair, DPF variation induces a nearly
50% magnitude change in the computed ⌬[HbR]. This
change is significant for t ⫽ 12 through 23 s (Student’s t
test, P ⬍ 0.05).
In Fig. 3, we compare the results from three subjects,
with a and b representing the two measurements from each
subject. Concentration changes were computed by subtracting t ⫽ 0 from an average of data from 10 to 12.4 s
following stimulus onset (a total of 30 data points). Each bar
in Fig. 3 represents the effect of altering the DPFs for the
three wavelength pairs for each measurement. In particular,
a bar represents the concentration change calculated using
the measured DPFs subtracted from the concentration
change calculated using the altered DPFs. Error bars represent the standard deviation of the 30 time points. It is clear
that DPF modulation strongly affects the calculated changes
in both [HbR] and [HbO2]. Importantly, in every case the
largest modulation and the most variability occurs when
pairing 830 nm with a wavelength higher than 770 nm, and
this difference is significant from the other wavelength pairs
in all cases (Student’s t tests, P ⬍ 0.02). We note that
significant task-related heart rate increases (⬃15 bpm) were
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recorded in two of the three subjects during the experiment.
However, the temporal profile of these changes did not
match that of the functional activation (being both delayed
3– 6 s from the activation rise and of a different shape), and
the optical signals and magnitudes differed across sourcedetector pairs. We therefore feel justified in inferring that
the reported changes include a significant contribution from
brain-related activation.
In the experiment just described, we found more noise
(random and systematic) in our HbR and HbO2 measures
when using 780 nm paired with 830 nm compared to other
wavelength pairs. To examine this further, we plotted the
absorption spectra for total hemoglobin (HbT ⫽ HbR ⫹
HbO2) as a function of tissue oxygen saturation (StO2, Fig.
4a) and the resulting theoretical sensitivity of saturation
measurements (as measured by ⌬␮a) to wavelength choice
(Fig. 4b). The latter curves are created by writing StO2 ⫽
HbO2/(HbR ⫹ HbO2) in terms of the components in Eq. (2)
and solving for ␮a1/␮a2 as a function of StO2. The steepness
of the curves in Fig. 4b indicates the sensitivity of the
calculated oxygen saturation to a measured change in the
ratio of ⌬␮a. Thus, a steep curve indicates that a small error
in the estimated ␮a ratio will produce a large error in
measured calculated oxygen saturation. Notice that the
780-nm curve is the steepest of the wavelengths we used
experimentally, suggesting that the 780- to 830-nm wavelength pair will be highly sensitive to all noise—systematic
or random—in the ␮a estimates. This is in agreement with
a recent publication indicating similar results in the presence of random noise (Yamashita et al., 2001). Fig. 4c
further shows that the sensitivity to cross-talk (governed by
parameters A, B, and D in Eq. (6)) grows quickly with
wavelengths greater than approximately 770 nm when
paired with 830 nm.
Theory and Monte Carlo simulations
We further examined the wavelength effect via Monte
Carlo simulation. Fig. 5a shows the results of an example
simulation as applied to our segmented head model using
optical properties for the tissue layers consistent with
830-nm light. Each contour represents a half order of magnitude change in the measured OD sensitivity to changes in
␮a, with the outermost contour representing a loss of five
orders of magnitude. Given our optical instrument sensitivity, we believe that we are sensitive to approximately the
outermost 1 cm of brain tissue. In Fig. 5b we display a
scaled version of the measured DPF along with the computed PPF for the white activation region shown in Fig. 5a,
as determined at 691, 752, 780, and 830 nm. It is clear that
the relative magnitudes of the PPF can differ from those of
the DPFs by 20% or more, depending on wavelength pair.
The behavior at 750 nm results from the fact that the PPF
for deep (1–2 cm down) focal activation is highly attenuated
by the absorption coefficient (which shows a small peak
around 750 nm), whereas the DPF is equally sensitive to
changes in absorption and scattering.
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G. Strangman et al. / NeuroImage 18 (2003) 865– 879
Fig. 3. Change in observed modulation depth of [HbO2] (top) and [HbR]
(bottom)—measured at the peak of the activation period (10 to 12.4 s from
the start of the stimulus)—when subtracting the modulation depth derived
from measured DPF values from the modulation depth derived from the
altered DPF. The bars thus indicate how much of an effect DPF has on
modulation depth, and the error bars are the standard deviation across 30
time points (2.4 s). Numbers 1–3 indicate subjects, and letters a and b
indicate the two measurements for each subject; the 780 – 830 bar for a
given subject is always significantly different from the other two bars
(Student’s test, P ⬍ 0.02).
Fig. 2. (a) Measured DPF at eight wavelengths for subject 1, along with altered DPFs at the four wavelengths considered in this paper (830 nm reduced by 10%; other
wavelengths increased by 10%). (b–d) ⌬[HbR] and ⌬[HbO2] for the same subject performing the motor task, computed using different, simultaneously collected wavelength
pairs. Pairs of curves were calculated from the measured and altered DPFs shown in (a). Standard errors at each point are on the order of 0.03 ␮M.
Fig. 6. Hemisphere comparison of two probe positions during the motor task, using 691 and 830 nm. (a) Time courses for ⌬[HbR] from EEG 10 –20 location
C3 (left primary sensorimotor cortex) and C4 (right primary sensorimotor cortex) during the motor task. (b) Time courses for ⌬[HbR] from location C3 and
C4 during the motor task in the same subject, after repositioning the optical probe by ⬃1 cm.
G. Strangman et al. / NeuroImage 18 (2003) 865– 879
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Fig. 4. (a) Overall hemoglobin absorption coefficient (HbR ⫹ HbO2) as a function of wavelength and oxygen saturation. Arrows indicate wavelengths
considered in the present study. (b) Hemoglobin saturation plotted against the ratio ⌬␮a(␭)/⌬␮a(830), for several wavelengths, ␭. Steeper curves indicate a
greater change in calculated saturation as a function of error in ⌬␮a. (c) Parameters A, B, and D from Eq. (6) are plotted for both HbO2 and HbR with ␭2
⫽ 830 nm. The curves are relatively flat up to approximately 770 nm, at which point the potential for cross-talk grows quickly.
Fig. 5. (a) Monte Carlo sensitivity profile at 830 nm overlain on the segmented brain, with “activated” voxels appearing in white. (b) A comparison of the
DPFs and PPFs for four different colors propagating through the geometry shown in (a). Uncertainty in the PPF owing to noise in the Monte Carlo simulation
is 5% (or ⬃0.005 units).
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G. Strangman et al. / NeuroImage 18 (2003) 865– 879
Fig. 7. Plots for the Monte Carlo simulations of medial–lateral position displacement. (a) The ratio of computed PPF to computed DPF as a function of the
source-detector pair location relative to the activated region. Measurements indicate distance from the center of the activated region, along the source-detector
line. Errors in the points at position 0, measured across five independent sets of Monte Carlo runs, were less than 1% of the PPF/DPF value. (b) Computed
partial volume of HbO2 (solid line, left y-axis; P in Eq. (6)) and cross-talk into HbO2 (dotted line, right y-axis; C/P in Eq. (6)) for each medial–lateral
source-detector position. Partial volume errors at position 0 averaged under 2%, and cross-talk errors at position 0 averaged 15% of the plotted value. (c)
Computed partial volume of HbR (solid line, left y-axis; P) and cross-talk into HbR (dotted line, right y-axis; C/P) for each medial–lateral source-detector
position. Partial volume and cross-talk errors for HbR resulting from the Monte Carlo simulations were comparable to those for HbO2.
Location of focal change
In Fig. 6, we consider experimentally the consequences
of repositioning the optical probe. Fig. 6a plots the response
to our motor task when recording bilaterally (over regions
C3 and C4, using just 691 and 830 nm). In this case,
recordings were made from 10 positions in each hemisphere
and the motor task was performed first with the right hand
and then with the left. The position with the largest response
from each hemisphere is plotted. Notice that the change in
[HbR] is largest over the right hemisphere (C3) regardless
of which hand was moving. Fig. 6b plots data from an
identical experimental run on the same subject, but with the
optical probe ⬃1 cm displaced from the position in Fig. 6a.
In this case, the side contralateral to the moving hand shows
the largest change in [HbR], which is more in line with
previous findings (e.g., Rao et al., 1993). (Results for HbO2
were similar, but with smaller wavelength-related differences, as would be expected given the larger amplitude of
HbO2 modulations; data not shown.)
Given this experimental evidence of substantial position
dependence when comparing across NIRS probes, suggested by prior theoretical arguments and empirical data
(Boas et al., 2001), we sought to quantify such effects. To
do so, we used Monte Carlo simulations to investigate the
cross-talk between oxy- and deoxyhemoglobin in a region
of activation as a function of the location of the recording
source-detector pair. To start, nine simulations were performed, each employing one source location (three colors of
light; we disregard 780 – 830 nm as a poor wavelength pair,
as indicated by Fig. 3) and one detector location. Simulations were rerun each time the source-detector probe was
moved 0.5 cm along the scalp in the medial–lateral direction
(i.e., parallel to the source-detector line) over the fixed
region of activation (cf. Figs. 1a and b). Fig. 7a shows the
ratio of the calculated DPF to the calculated PPF for each of
these nine positions at each of the three experimentally used
wavelengths. Notice that this ratio is much closer to zero
than to one, indicating that the PPF through the focal region
is small relative to the DPF. As would be expected, the
largest PPF occurs when there is minimal offset between the
activation focus and the center of the source-detector pair
and falls off rapidly with displacement. The fall-off suggests
that a “miss” of slightly more than 1 cm would result in a
50% drop in sensitivity to the focal concentration change.
The standard deviation in the PPF/DPF ratio across five
independent Monte Carlo runs at position 0 was 0.6, 0.7,
0.3, and 0.9% of that ratio for 691, 760, 780, and 830 nm,
respectively (that is, error bars are smaller than the size of
the data point).
Figs. 7b and c plot the partial volumes (P in Eq. (6)) and
cross-talk (C in Eq. (6), plotted as a proportion of P, i.e.,
C/P) obtained from the Monte Carlo simulations for HbO2
(Fig. 7b) and HbR (Fig. 7c) as calculated from both the 752to 830-nm wavelength pair (results were essentially identical for the 691- to 830-nm pair). The partial volumes (measured via the left-hand y-axis) simply follow the PPF/DPF
ratio, peaking at 0 cm offset. (The standard deviation in the
partial volume of HbR and HbO2, again across five Monte
Carlo runs, at position 0 ranged from 0.7% to 1.7% of the
partial volume.) Examining the cross-talk curves (dotted
lines, right-hand y-axis), the cross-talk into both species is
essentially flat and comprises less than 5% of the partial
volume effect, up to a lateral displacement of ⬃1 cm. To
elaborate, recall that the parameter C represents the proportion of the other species cross-talking into the species of
interest. (If C ⫽ 0.1 then, for example, 10% of the real
⌬[HbO2] would be added to the measured ⌬[HbR] and vice
versa. Notice that this could be a large relative error in, e.g.,
⌬[HbR] if the real ⌬[HbO2] is much greater than the real
⌬[HbR].) Instead of plotting C directly, we more generally
plot C/P to show how large this cross-talk effect is relative
G. Strangman et al. / NeuroImage 18 (2003) 865– 879
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Fig. 8. Plots for the Monte Carlo simulations of anterior–posterior position displacement. (a) The ratio of computed PPF to computed DPF as a function of
the source-detector pair location relative to the activated region. Measurements indicate distance from the center of the activated region, along the
source-detector line. (b) Computed partial volume of HbO2 (solid line, left y-axis; P in Eq. (6)) and cross-talk into HbO2 (dotted line, right y-axis; C/P in
Eq. (6)) for each anterior–posterior source-detector position. (c) Computed partial volume of HbR, P, and cross-talk into HbR, C, for each anterior–posterior
source-detector position; same legend as for (b). Errors are comparable to those reported in Fig. 7.
to the partial volume effect. We do this because noninvasive
concentration measurements will typically be strongly affected (attenuated) by the partial volume effect, and we
want to determine what proportional error in the measured
concentration can be attributed specifically to cross-talk. In
an experimental situation where the center of the sourcedetector line lies within 1 cm of the measured activation,
this proportional error owing to cross-talk should be less
than ⬃5%. However, the magnitude of the cross-talk still
depends on the relative magnitudes of the real ⌬[HbR] and
⌬[HbO2] and thus 5% of the ⌬[HbO2] may be a large
fraction of the ⌬[HbR]. That is, in Eq. (5) C could be a small
proportion of P but still contribute substantial error to the
measured species of interest, depending on the real concentration changes in the other species. The remaining crosstalk (C/P) curves can be interpreted in exactly this manner.
(The standard deviation in cross-talk across Monte Carlo
runs at position 0 averaged 15% of the plotted cross-talk
value.)
Fig. 8 shows the same information as Fig. 7, but for
anterior–posterior movement of the source-detector pair
(again with three colors). That is, the probe remained centered medial–laterally over the activation, but was moved
“through” the plane shown in Figs. 1a and b. Results are
quite similar except that the raw signal and partial volumes
fall off somewhat more rapidly in this transverse direction
(to 50% of maximum in slightly less than 1 cm). The
cross-talk remains similar (⬃5% for small offsets).
Hemoglobin species distribution
We next used Monte Carlo simulations to examine the
possibility of a spatial distribution mismatch between HbR
and HbO2—namely, that changes in HbR are more localized
than changes in HbO2. Fig. 9a plots the ratio of calculated
PPF/DPF as the spatial extent of the HbO2 change is increased beyond the (static) boundary of the HbR change (in
1-mm rectangular shells). As the HbO2 change becomes
larger, the ratio should approach 1, because the HbO2
change is approaching the DPF assumption of a global
Fig. 9. Plots for the Monte Carlo simulations of hemoglobin species volume. (a) The ratio of computed PPF to computed DPF as a function of the size of
the region of HbO2 concentration change. (b) Computed partial volume of HbO2 (solid line, left y-axis; P in Eq. (6)) and cross-talk into HbO2 (dotted lines
(691 and 752 nm), right y-axis; C/P in Eq. (6)) for different sized regions of HbO2 concentration change. (c) Computed partial volume of HbR (solid line,
left y-axis; P) and cross-talk into HbR (dotted lines (691 and 752 nm), right y-axis; C/P) for different sized regions of HbO2 concentration change.
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G. Strangman et al. / NeuroImage 18 (2003) 865– 879
Fig. 10. Plots for the Monte Carlo simulations of a secondary activation focus. (a) Computed partial volume of HbO2 (solid line, left y-axis; P in Eq. (6))
and cross-talk into HbO2 (dotted line, right y-axis; C/P in Eq. (6)) for different secondary activation locations. (b) Computed partial volume of HbR (solid
line, left y-axis; P) and cross-talk into HbR (dotted line, right y-axis; C/P) for different secondary activation locations. Locations 1–5 represent movements
of the secondary region 5 mm medial and 2.5 mm superior from the previous region, starting from the primary activation’s location.
change. While the HbO2 activation is quite large at the
farthest extreme we considered (HbO2 volume 3560 mm3),
the ratio is nevertheless far from a ratio of 1, indicating that
the assumption of global activation is still strongly violated
because of the overlying scalp and skull.
Figs. 9b and c again plot the computed partial volume (P)
and cross-talk (plotted as C/P) for HbO2 (Fig. 9b) and HbR
(Fig. 9c). The partial volume for HbO2 increases as the
HbO2 activation region grows, whereas the partial volume
for HbR is essentially flat. Departures from flat in the solid
line in Fig. 9c demonstrate the small amount of noise generated by random number seeds in our simulations. The
magnitudes of the cross-talk are considerably larger in this
case than for location. The rough downward trend for crosstalk into HbO2 arises because an essentially flat cross-talk is
being divided by the increasing partial volume. It is apparent that wavelength choice more strongly modulates crosstalk here, by 25%–50% into HbO2 and by 200%–300% into
HbR. Interestingly, no single wavelength has the least crosstalk in both species.
Multiple activation regions
Finally, we considered the possibility that a second region of activation could be within the field of view of the
NIRS probe during a given recording. The partial volume
for the activation region centered between the source and
detector and the within-region cross-talk is precisely the
same as in Figs. 7–9. In Fig. 10, therefore, we simply plot
the computed partial volume and cross-talk for HbO2 and
HbR (Figs. 10a and b, respectively) for the secondary activation, divided by the partial volume for HbO2 and HbR for
the primary, centered activation (that is P␤/P␣, where ␤
represents the secondary activation and ␣ denotes the primary activation centered below and between the sourcedetector pair). Thus, at the closest secondary position, the
partial volume of the secondary region is greater than 50%
of the partial volume of the primary activation. The associ-
ated species’ sensitivity to cross-talk resulting from the
second activation was also normalized to the partial volume
of the primary activation or C␤/P␣. Thus, the cross-talk into
HbO2 induced by the second activation focus is approximately 3% of the expected HbO2 concentration change
when it is within ⬃5 mm of the main focus and drops to
below 1% beyond the second position (11 mm from the
primary activation). The cross-talk into HbR induced by the
second activation is just over 1% of the expected HbR
concentration change at the first position and quickly falls
toward zero. This occurs for 752 nm as well (not shown).
Discussion
Reliable quantitation of HbR and HbO2 concentrations
using the standard approach to analyzing NIRS data is prone
to a variety of systematic errors when recordings involve
focal chromophore changes. For functional brain recordings, central among these errors is cross-talk between calculated HbR and HbO2 concentrations consequent to the
focal nature of the chromophore changes. In particular, if a
change is focal, the relevant parameter for calculating the
actual concentration change is the partial pathlength—the
distance the light travels through the activated region and
not the total distance the light travels from source to detector. An optical measurement will be prone to cross-talk
whenever assumptions about the PPFs differ from the actual
PPFs. For each of the four systematic errors we have described, however, there are at least partial solutions that help
to minimize such cross-talk.
Wavelength selection
One partial solution is the choice of measurement wavelengths and recording position. Referring back to Fig. 4, it
is clear that the 780- to 830-nm wavelength pair will be a
less optimal choice for oxygen saturation related measure-
G. Strangman et al. / NeuroImage 18 (2003) 865– 879
ments, because a relatively small error in the measured
absorption coefficient can produce a large error in the calculated saturation. This conclusion is supported by the experimental data in Fig. 3. Avoiding this wavelength pair can
therefore help minimize differential sensitivity in a focalchange situation. Note that this conclusion holds even
though wavelengths in this range will have substantially
overlapping spatial sensitivities to the underlying tissue.
Given a measurement with an infinite signal-to-noise ratio,
cross-talk would indeed be minimized by choosing wavelengths with overlapping spatial sensitivities. However, the
present findings indicate that the sensitivity to measurement
error in this wavelength range (cf. Fig. 4) is large enough to
nullify any cross-talk reduction obtained by having overlapping spatial sensitivities.
Importantly, employing more than two wavelengths—
including full-spectrum approaches—will not avoid the
problem. Any concentration calculation that includes data
from 830 nm and a wavelength in the range of roughly
770 – 800 nm will provide noisy information about the actual concentration change, as shown previously (Yamashita
et al., 2001). Although we have not investigated this systematically, Fig. 4c suggests that any pair of wavelengths
between ⬃770 and 850 nm would result in similar noise
issues, consequent to the small absorption spectra differences in this range. Any such noisy information will effectively be averaged together with less-noisy data from other
wavelengths, reducing the validity of the concentration calculations compared to simply excluding data from any
wavelengths in the 770- to 800-nm range.
Location of focal change
A more general solution to the NIRS cross-talk problem
is to replace the standard DPFs with PPFs—that is, to
account for the partial pathlength through the activated
region. However, the location and extent of activation are
typically unknown (and, in fact, often comprise a parameter
of interest to the study). General statements can be made,
however, even for the complicated internal tissue structure
of the head. To start, it appears reasonable to assume that
the activation region is indeed located below and between
the source-detector pair. Experimental and theoretical results suggest that signal levels drop substantially when “off
target” in either the longitudinal or the transverse directions
by more than 1 cm. At the same time, species-related crosstalk was relatively stable out to 1.5–2 cm off center. Thus,
when the activation is sufficiently off center for cross-talk to
rise above a few percent, the signals will typically be weak.
The existence of cross-talk from HbO2 into HbR on the
order of a few percent, however, can still be substantial
depending on the observed magnitude HbO2 change—a
large change in HbO2 coincident with a small change in
HbR could induce 100% (or more) relative error in HbR.
This consequence of course depends on the changes re-
877
corded in the particular experimental results and paradigm
in question. It does appear that the relative magnitude of this
cross-talk is stable (for these wavelengths) when the probe
is within a ⬃1-cm radius of the optimal source-detector
sampling region. Hence, an experimental procedure of finding the optical probe position that maximizes signal modulation should help minimize the effects of location-related
cross-talk. The magnitude of our errors are in substantial
agreement with the focal-activation findings recently published by Uludag et al. (2002) which specifically consider a
760- to 830-nm wavelength pairing. (Our error estimates
tend to be slightly larger as a result of assuming a somewhat
deeper region of focal concentration change.)
Minimizing location-related cross-talk, however, does
not imply elimination of undesirable cross-talk effects. This
is particularly important with regard to comparing across
detectors in a NIRS experiment. Often it is desirable to
demonstrate differential hemispheric lateralization for a task
(e.g., when studying language tasks, visual hemi field tasks,
and motor function with hand alternation). As was shown in
Fig. 6, however, comparison across NIRS probes (in this
case, across two hemispheres) should be undertaken with
caution. The results in Fig. 6a, obtained by selecting the
largest response of 10 positions in that hemisphere, obviously contradict those from Fig. 6b, which were obtained in
the same way. In general, therefore, comparing amplitudes
across NIRS probes is not a valid comparison. The only way
to compare across spatial regions with reasonable confidence is to employ diffuse optical imaging wherein all
optical measurements are evaluated for self-consistency.
Species distribution and multiple foci
We have also argued that two additional issues have the
potential to affect cross-talk: a lack of colocalized changes
in HbO2 and HbR concentrations and the possibility of
simultaneously detecting changes from two or more activated regions via a single source-detector pair. For noncoincident concentration changes, we found that the cross-talk
was again less than 10% of the partial volume effect, over
the extreme range of activation sizes investigated (again
excluding 780 nm). We did not, however, investigate the
situation wherein overlying tissues (e.g., scalp) show an
increase in HbO2, as might be expected when heart rate and
blood pressure increases during a difficult task. Given that
such changes are closer to the source and detector, they
could have substantial effects on calculated concentrations,
as has been argued elsewhere (Firbank et al., 1998).
For our dual-activation simulations, we found that, in
addition to a few percent of within-focus cross-talk, there
can be cross-talk on the order of a few more percent when
a second region of activation is closer than 1 cm. If the
second activation is more than 1 cm away, the betweenfocus cross-talk is likely to remain negligible.
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G. Strangman et al. / NeuroImage 18 (2003) 865– 879
Conclusions
NIRS recordings are potentially sensitive to several
sources of systematic error, and such errors can be substantial in the cases of dramatic differences in concentration
changes (especially cross-talk into HbR when ⌬[HbO2] ⬎⬎
⌬[HbR]). However, there are ways to minimize such errors.
One way of doing so is choosing wavelengths appropriate
for the preparation. In a NIRS recording setting, at least
where focal changes are expected, pairing 780 nm with 830
nm is inferior for measuring oxygenation changes compared
to pairing 690 or 760 nm with 830 nm. Theoretical considerations suggested that in fact all wavelengths in the 770- to
800-nm range will provide similarly poor oxygenation information. A secondary solution is to position probes as
close as possible to the location of change—which is typically achieved by selecting a recording location to maximize signal contrast. Our findings indicate that these approaches can limit such errors to a small fraction (⬍10%) of
the observed concentration changes. Implementing these
approaches, plus an awareness of the appropriate magnitude
of any remaining errors, should afford stronger interpretation of NIRS recording data than has heretofore been possible. In particular, we believe these findings can help avoid
under- or overinterpretation of small measured concentration changes (especially in HbR) from future NIRS experiments.
Acknowledgments
We thank Shalini Nadgir for technical assistance during
the in vivo measurements. We acknowledge support from
the NINDS (F32-NS10567 and R29-NS38842), NCRR
(P41-RR14075), NIMH (R01-MH62854), and the National
Space Biomedical Research Institute through NASA Cooperative Agreement NCC 9-58. This research was funded in
part by the US Army, under Cooperative Agreement
DAMD17-99-2-9001. This publication does not necessarily
reflect the position or the policy of the Government, and no
official endorsement should be inferred.
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